h = dual f
The map $f : C \to D$ of chain complexes over the ring $S$ induces the map $h = Hom(f, S^1) : Hom(D, S^1) \to Hom(C,S^1)$ defined by $\phi \mapsto \phi f$.
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This routine is functorial.
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For backwards compatibility, one can also use transpose.
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The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/Complexes/ChainComplexMapDoc.m2:1314:0.